CN109084800B - Moving body path planning method under multi-station relay navigation based on space compression - Google Patents

Moving body path planning method under multi-station relay navigation based on space compression Download PDF

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CN109084800B
CN109084800B CN201811181117.9A CN201811181117A CN109084800B CN 109084800 B CN109084800 B CN 109084800B CN 201811181117 A CN201811181117 A CN 201811181117A CN 109084800 B CN109084800 B CN 109084800B
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CN109084800A (en
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窦丽华
漆鸣凤
辛斌
陈杰
陈晨
白永强
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34—Route searching; Route guidance
    • G01C21/3407—Route searching; Route guidance specially adapted for specific applications
    • G01C21/3415—Dynamic re-routing, e.g. recalculating the route when the user deviates from calculated route or after detecting real-time traffic data or accidents
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34—Route searching; Route guidance
    • G01C21/3446—Details of route searching algorithms, e.g. Dijkstra, A*, arc-flags, using precalculated routes

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Abstract

The invention discloses a moving body path planning method under multi-station relay navigation based on space compression, which adopts a region coding mode to code waypoints, wherein the positions of the waypoints can be uniquely represented by two-dimensional coordinates under a local rectangular coordinate system, and the region coding method can represent the positions of any points in an eye-shaped cross connection area and has wide applicability; according to the geometric relation between the navigation handover constraint threshold value and the position and effective acting radius of the navigation station, the value range of the horizontal coordinates of the waypoints is compressed, partial infeasible solutions violating the navigation handover constraint are directly removed before the path planning algorithm is operated, the path planning space is reduced, and the path planning algorithm is facilitated to find high-quality feasible solutions more quickly.

Description

Moving body path planning method under multi-station relay navigation based on space compression
Technical Field
The invention belongs to the field of moving body path planning research, and particularly relates to a moving body path planning method under multi-station relay navigation based on space compression.
Background
The multi-station relay navigation is a joint navigation method for successively navigating a moving body by a plurality of navigation stations which are scattered at different spatial positions and can cover a larger space in a navigation action range. The moving body relies on an external navigation station to provide it with position information or control commands. Compared with other navigation modes, the self navigation mode (such as inertial navigation) of the moving body has limited precision, the satellite navigation mode is easy to damage and has high manufacturing cost, and the multi-station relay navigation mode not only has strong reliability, but also can provide path guidance for the moving body to execute remote tasks in the multi-station combined relay navigation mode, thereby effectively extending the controllable moving range of the moving body.
The problem of moving body path planning under multi-station relay navigation is a key problem to be solved for realizing the advanced navigation mode with frontier performance. The multi-station relay navigation technology imposes two special constraint conditions for path planning of a moving body: 1) the navigation range constraint is that the whole path of the motion body from the starting point to the end point is required to be positioned in the effective action range of the navigation station; 2) the navigation handover constraint, i.e. the shortest path length of the moving body in the handover area (the overlapping area of the effective action areas of the two navigation stations) must be greater than a certain value to ensure that the navigation right of the moving body is successfully handed over from one station to the other.
Disclosure of Invention
The invention provides a moving body path planning method under multi-station relay navigation based on space compression, which reduces the path planning space and is beneficial to a path planning algorithm to find a feasible solution with high quality more quickly.
A moving body path planning method under multi-station relay navigation based on space compression is characterized by comprising the following steps:
step 1, inputting a starting point position, an end point position, a navigation handover constraint threshold value, positions of a plurality of navigation stations and effective acting radiuses of a moving body; the effective range of the navigation station is represented by a circular area; defining the navigation handover constraint threshold as: in order to ensure the navigation handover success, the minimum path length of the moving body in the handover area is determined; the handover area is an overlapping area of effective action ranges of two navigation stations;
one path is formed by sequentially connecting waypoints comprising a starting point, a plurality of intermediate waypoints and a terminal point, and the waypoints are connected by adopting straight line segments; defining an intermediate waypoint comprising a starting junction and an ending junction of all the junction areas; the starting intersection point represents the position where the next navigation station starts to provide navigation information for the moving body, the ending intersection point represents the position where the previous navigation station stops providing navigation information for the moving body, and the navigation information of the moving body is provided by the two navigation stations together between the starting intersection point and the ending intersection point and the transfer of the navigation right of the moving body is completed; one path is jointly represented by the positions of all intermediate waypoints;
step 2, coding the intermediate waypoints by adopting a regional coding mode, wherein the starting intersection point and the ending intersection point are positioned at any positions in the intersection region;
defining two end points of an arc entering into the handover area, which are also two end points of an arc exiting out of the handover area, and the two end points are two top points of the handover area; establishing a local rectangular coordinate system by taking the middle point of a connecting line of two vertexes of the handover area as an origin, wherein the positive direction of the Y ' axis is the direction in which the position of the previous navigation station corresponding to the handover area points to the position of the next navigation station, and the positive direction of the X ' axis points to the right side from the left side of the Y ' axis; the positions of the start and end junctions are uniquely represented by two-dimensional coordinates (x ', y') in the local rectangular coordinate system;
respectively determining the value ranges of two coordinates of the starting junction and the ending junction:
wherein, the value range of the x' coordinate is as follows: under the local rectangular coordinate, if the arc entering and the arc exiting of the cross-connection area are both minor arcs, the value range of the x' coordinate is
Figure BDA0001824744430000021
Wherein A and B are two vertices of the handover region; if one of the arc-in and arc-out is not inferior, the value range of the x' coordinate is [ -min (R)1,R2),min(R1,R2)](ii) a Wherein R is1And R2Effective acting radii of a navigation station and a next navigation station in a handover area are respectively;
the value range of the y' coordinate is as follows: and taking projection points of the starting intersection point and the ending intersection point on an X ' axis as a vertical foot as auxiliary lines, intersecting two points with a boundary arc of the intersection area, wherein coordinate values of the two points on a Y ' axis are the maximum value and the minimum value of the Y ' coordinates of the starting intersection point and the ending intersection point.
Step 3, compressing the value ranges of the x' coordinates of the starting junction and the ending junction according to the geometric relation between the navigation cross-connection constraint threshold and the position and effective acting radius of the navigation station, and directly eliminating partial infeasible solutions violating the navigation cross-connection constraint;
and 4, planning a path based on the compressed regional coding path planning space obtained in the step 3, and optimizing the position of the middle waypoint.
Preferably, in step 3, the method for compressing the value range of the x' coordinates of the start junction and the end junction is as follows:
s300, setting the positions of any two adjacent navigation stations as OjAnd Oj+1Radius is R respectivelyjAnd Rj+1Cross over to point Aj(vector quantity)
Figure BDA0001824744430000031
Left side) and point Bj(vector quantity)
Figure BDA0001824744430000032
Right side), point CjIs the mid-point of the arc, point DjIs the arc-out midpoint;
s301, calculating an x' coordinate set of points on an input arc, wherein the points meet the condition that the longest distance to the boundary of a handover area is not less than a navigation handover constraint threshold value:
case 1: the arc inlet and the arc outlet are minor arcs:
case 1-A: the mid point of the incoming arc is on the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint threshold is met
Figure BDA0001824744430000033
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000034
Wherein
Figure BDA0001824744430000035
Is point AjThe x' coordinate value of (a) is,
Figure BDA0001824744430000036
is point BjX' coordinate value of (a);
② if the navigation handover constraint threshold is met
Figure BDA0001824744430000037
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000038
Wherein
Figure BDA0001824744430000039
Is point Fj,1The x' coordinate value of (a) is,
Figure BDA00018247444300000310
is point Fj,2X' coordinate value of (a); at point BjAs a circle center, LjMaking a circle with a radius, the intersection point of which with the arc is point Fj,1(ii) a At point AjAs a circle center, LjMaking a circle with a radius, the intersection point of which with the arc is point Fj,2；
③ if the navigation handover constraint threshold is met
Figure BDA0001824744430000041
Then the x' coordinate set of the point on the arc meeting the requirement that the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
case 1-B: the midpoint of the arc is not in the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint threshold is met
Figure BDA0001824744430000042
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000043
② if the navigation handover constraint threshold is met
Figure BDA0001824744430000044
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000045
Wherein, point Gj,1Is ray BjOjThe point of intersection with the incoming arc,
Figure BDA0001824744430000046
is point Hj,1The x' coordinate value of (a) is,
Figure BDA0001824744430000047
is point Hj,2X' coordinate value of (a); at point OjAs a circle center, Lj-RjMaking a circle with a radius, the intersection point of the circle and the arc is a point Hj,1(distance point A)jNearer) and point Hj,2(distance point A)jFarther);
③ if the NAV Handover constraint threshold is met
Figure BDA0001824744430000048
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000049
④ if the navigation handover constraint threshold is met
Figure BDA00018247444300000410
Then the x' coordinate set of the point on the arc meeting the requirement that the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
case 2: the arc is inferior arc, and the arc is superior arc:
① if the navigation handover constraint threshold is met
Figure BDA00018247444300000411
The x' coordinate set of points on the arc that satisfy the "longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is [ -R [)j,Rj]；
② if the navigation handover constraint threshold is met
Figure BDA00018247444300000412
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000051
③ if the navigation handover constraint threshold satisfies Lj>2RjIf the distance to the boundary of the handover area is not less than the navigation handover constraint threshold, the x' coordinate set of the point on the arc is an empty set;
case 3: the arc is a major arc, and the arc is a minor arc:
① if the navigation handover constraint threshold is met
Figure BDA0001824744430000052
The x' coordinate set of points on the arc that satisfy the "longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is [ -R [)j+1,Rj+1]；
② if the navigation handover constraint threshold is met
Figure BDA0001824744430000053
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000054
③ if the navigation handover constraint threshold is met
Figure BDA0001824744430000055
Then the longest distance on the arc entry that satisfies "to the boundary of the handover area is not less than the navigationSet of x' coordinates of points of the handover constraint threshold as
Figure BDA0001824744430000056
Wherein
Figure BDA0001824744430000057
Is point Jj,2The x' coordinate value of (a) is,
Figure BDA0001824744430000058
is point Jj,3X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is a point Jj,1(distance point A)jNearer) and point Jj,2(distance point A)jFarther); at point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is a point Jj,3(distance point A)jNearer) and point Jj,4(distance point A)jFarther);
④ if the navigation handover constraint threshold satisfies Lj>2Rj+1If the distance to the boundary of the handover area is not less than the navigation handover constraint threshold, the x' coordinate set of the point on the arc is an empty set;
s302, calculating an x' coordinate set of points on the arc, wherein the points meet the condition that the longest distance from the boundary of the handover area is not less than a navigation handover constraint threshold value:
case 1: the outgoing arc and the incoming arc are both minor arcs:
case 1-A: the midpoint of the arc is on the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint threshold is met
Figure BDA0001824744430000059
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000061
② if the navigation handover constraint threshold is met
Figure BDA0001824744430000062
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000063
Wherein
Figure BDA0001824744430000064
Is of point F'j,1The x' coordinate value of (a) is,
Figure BDA0001824744430000065
is of point F'j，2X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point F'j,1(ii) a At point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point F'j，2；
③ if the navigation handover constraint threshold is met
Figure BDA0001824744430000066
Then the x' coordinate set of the point on the outgoing arc which meets the condition that the longest distance from the boundary of the handover area is not less than the navigation handover constraint threshold value is an empty set;
case 1-B: the midpoint of the arc is not in the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint threshold is met
Figure BDA0001824744430000067
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000068
② if the navigation handover constraint threshold is met
Figure BDA0001824744430000069
Then "to hand-over" is satisfied on the outgoing arcThe x' coordinate set of the point where the longest distance of the area boundary is not less than the navigation handover constraint threshold is
Figure BDA00018247444300000610
Wherein, point G'j,1Is ray BjOj+1The point of intersection with the outgoing arc,
Figure BDA00018247444300000611
is H'j,1The x' coordinate value of (a) is,
Figure BDA00018247444300000612
is H'j,2X' coordinate value of (a); at point Oj+1As a circle center, Lj-Rj+1Is a circle with a radius, and the intersection point of the circle and the arc is a point H'j,1(distance point A)jNearer) and point H'j,2(distance point A)jFarther);
③ if the navigation handover constraint threshold is met
Figure BDA00018247444300000613
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA00018247444300000614
④ if the navigation handover constraint threshold is met
Figure BDA00018247444300000615
Then the x' coordinate set of the point on the outgoing arc which meets the condition that the longest distance from the boundary of the handover area is not less than the navigation handover constraint threshold value is an empty set;
case 2: the arc outlet is a minor arc, and the arc inlet is a major arc:
① if the navigation handover constraint threshold is met
Figure BDA0001824744430000071
The set of x' coordinates of points on the outgoing arc that satisfy the "longest distance to the boundary of the handover area is not less than the navigation handover constraint thresholdIs [ -R ]j+1,Rj+1]；
② if the navigation handover constraint threshold is met
Figure BDA0001824744430000072
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000073
③ if the navigation handover constraint threshold satisfies Lj>2Rj+1If so, the x' coordinate set of the point on the outgoing arc meeting the condition that the longest distance from the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
case 3: the outgoing arc is a major arc, and the incoming arc is a minor arc:
① if the navigation handover constraint threshold is met
Figure BDA0001824744430000074
The x' coordinate set of points on the outgoing arc that satisfy "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is [ -Rj,Rj]；
② if the navigation handover constraint threshold is met
Figure BDA0001824744430000075
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000076
③ if the navigation handover constraint threshold is met
Figure BDA0001824744430000077
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure BDA0001824744430000078
Wherein
Figure BDA0001824744430000079
Is Point J'j,2The x' coordinate value of (a) is,
Figure BDA00018247444300000710
is Point J'j,3X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point J'j,1(distance point A)jNearer) and point J'j,2(distance point A)jFarther); at point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point J'j,3(distance point A)jNearer) and point J'j,4(distance point A)jFarther);
④ if the navigation handover constraint threshold satisfies Lj>2RjIf so, the x' coordinate set of the point on the outgoing arc meeting the condition that the longest distance from the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
and S303, calculating a union of the two x 'coordinate sets obtained in the steps S301 and S302, namely a value range after compression of the x' coordinates of the starting junction and the ending junction.
The invention has the beneficial effects that:
the moving body path planning method under the multi-station relay navigation based on the space compression adopts a region coding mode to code the waypoints, the positions of the waypoints can be uniquely represented by two-dimensional coordinates under a local rectangular coordinate system, the position of any point in an eye-shaped intersection region can be represented by the region coding method, and the method has wide applicability; according to the geometric relation between the navigation handover constraint threshold value and the position and effective acting radius of the navigation station, the value range of the horizontal coordinates of the waypoints is compressed, partial infeasible solutions violating the navigation handover constraint are directly removed before the path planning algorithm is operated, the path planning space is reduced, and the path planning algorithm is facilitated to find high-quality feasible solutions more quickly.
Drawings
FIG. 1 is a flow chart of a path planning method of the present invention;
FIG. 2 is an exemplary diagram of a path;
FIG. 3 is a schematic diagram of region coding; wherein, in FIG. 3(a), when the arc entering and the arc exiting are both inferior arcs, FIG. 3(b) shows that the arc entering is inferior arc, and when the arc exiting is superior arc, FIG. 3(c) shows that the arc entering is superior arc, and the arc exiting is inferior arc;
FIG. 4 is a schematic view of case 1-A of computing the set of x' coordinates of a point on the arc that satisfies the condition;
FIG. 5 is a schematic view of case 1-B of computing a set of x' coordinates of a point on an arc that satisfies a condition;
FIG. 6 is a schematic view of case 2 of computing a set of x' coordinates of a point on the arc that satisfies a condition;
FIG. 7 is a schematic view of case 3 of computing the set of x' coordinates of a point on the arc that satisfies the condition;
FIG. 8 is a schematic view of case 1-A of computing a set of x' coordinates for a point on the arc that satisfies a condition;
FIG. 9 is a schematic view of case 1-B of computing a set of x' coordinates of a point on an arc that satisfies a condition;
FIG. 10 is a schematic diagram of case 2 of computing a set of x' coordinates of a point on an arc that satisfies a condition;
FIG. 11 is a schematic diagram of case 3 of computing a set of x' coordinates for a point on an arc that satisfies a condition;
fig. 12 is a schematic view of an embodiment.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
The invention is realized by the following technical scheme, as shown in figure 1, comprising the following steps:
step 1, inputting the starting point position W of the moving bodysThe end point position WdAnd a navigation handover constraint threshold value L ═ L1,L2,...,LN-1](N is the number of navigation stations), positions of a plurality of navigation stations Oi(i ═ 1,2,. cndot., N) and effective radius Ri(i ═ 1,2,. cndot., N); circular area S for effective range of navigation stationi(i ═ 1, 2.., N); navigation handover constraint means that the moving body is in order to ensure successful navigation handoverHandover area HjThe link length in (j-1, 2.. N-1) must not be less than a set threshold L ═ L1,L2,...,LN-1]The area of the handover is the overlapping area of the effective ranges of the two navigation stations, i.e. Hj＝Sj∩Sj+1；
One path is formed by sequentially connecting waypoints comprising a starting point, a plurality of intermediate waypoints and an end point, the waypoints are connected by straight line segments, and an exemplary path is shown in figure 2; defining an intermediate waypoint including the starting point W of all handover areas2j-1(j ═ 1, 2.., N-1) and end intersection point W2j(j ═ 1,2,. N-1); the starting intersection point represents the position where the next navigation station starts to provide navigation information for the moving body, the ending intersection point represents the position where the previous navigation station stops providing navigation information for the moving body, and the navigation information of the moving body is provided by the two navigation stations together between the starting intersection point and the ending intersection point and the transfer of the navigation right of the moving body is completed; since the starting and ending positions are known, a path can be represented by the position union of all intermediate waypoints, i.e., p ═ W1,W2,...,W2N-2]；
Step 2, coding the intermediate waypoints by adopting a regional coding mode, wherein the starting intersection point and the ending intersection point can be positioned at any position in the intersection region; the schematic diagram of the region encoding method is shown in FIG. 3, wherein the circular region SjAnd a circular region Sj+1Cross over at point AjAnd point BjThe centers of circles are respectively OjAnd Oj+1Radius is R respectivelyjAnd Rj+1(ii) a Point EjIs line segment AjBjA midpoint of (a);
for handover area HjStart of intersection W2j-1The region coding method comprises the following steps: at point EjAs the origin, the positive direction of the Y' axis is parallel to the vector
Figure BDA0001824744430000101
The positive direction of the X 'axis points to the right side from the left side of the Y' axis, a local rectangular coordinate system is established, and then W2j-1Can be determined by two-dimensional coordinates under the local rectangular coordinate system
Figure BDA0001824744430000102
A unique representation;
in the local rectangular coordinates, if the incoming arc and the outgoing arc are both minor arcs (as shown in fig. 3 (a)), the arc is determined to be a minor arc
Figure BDA0001824744430000103
Figure BDA0001824744430000104
Is dependent on
Figure BDA0001824744430000105
Value of (2) in points
Figure BDA0001824744430000106
Making auxiliary lines for the foot drop, and respectively crossing the arc-in and arc-out of the cross-over area at the point M2j-1,1And point M2j-1,2Then, then
Figure BDA0001824744430000107
Under the local rectangular coordinates, if the incoming arc is a minor arc and the outgoing arc is a major arc (as shown in fig. 3 (b)), the local rectangular coordinates are obtained
Figure BDA0001824744430000108
Figure BDA0001824744430000109
Is dependent on
Figure BDA00018247444300001010
Value of (2) in points
Figure BDA00018247444300001011
The foot drop is taken as an auxiliary line; when in use
Figure BDA00018247444300001012
Then the auxiliary line and the arc entering and exiting of the connection area are respectively crossed at the point M2j-1,1And point M2j-1,2Otherwise, the auxiliary line is only crossed withThe arc of the contact region intersects at a point M2j-1,1And point M2j-1,2；
Figure BDA00018247444300001013
Under the local rectangular coordinate, if the incoming arc is a good arc and the outgoing arc is a bad arc (as shown in fig. 3 (c)), the local rectangular coordinate is used for determining whether the incoming arc is a good arc or a bad arc
Figure BDA00018247444300001014
Figure BDA00018247444300001015
Is dependent on
Figure BDA00018247444300001016
Value of (2) in points
Figure BDA00018247444300001017
The foot drop is taken as an auxiliary line; when in use
Figure BDA00018247444300001018
Then the auxiliary line and the arc entering and exiting of the connection area are respectively crossed at the point M2j-1,1And point M2j-1,2Otherwise, the auxiliary line only intersects with the arc entering of the handover area at the point M2j-1,1And point M2j-1,2；
Figure BDA00018247444300001019
For handover area HjEnd the junction W2jRegion coding method and value range and starting intersection point W2j-1The region coding method and the value range are completely the same;
step 3, compressing according to the geometric relation between the navigation handover constraint threshold value and the position and effective acting radius of the navigation station
Figure BDA00018247444300001020
And
Figure BDA00018247444300001021
value range of (1), directly rejectingExcept for some infeasible solutions that violate navigation handover constraints; compression
Figure BDA0001824744430000111
And
Figure BDA0001824744430000112
the value range method is as follows:
s300, setting the positions of any two adjacent navigation stations as OjAnd Oj+1Radius is R respectivelyjAnd Rj+1Cross over to point Aj(vector quantity)
Figure BDA0001824744430000113
Left side) and point Bj(vector quantity)
Figure BDA0001824744430000114
Right side); point CjIs the mid-point of the arc, point DjIs the arc-out midpoint;
s301, calculating an x' coordinate set omega of a point on an input arc, wherein the point meets the condition that the longest distance to the boundary of a handover area is not less than a navigation handover constraint threshold1：
Case 1: arc entry
Figure BDA0001824744430000115
And out of arc
Figure BDA0001824744430000116
Are minor arcs:
case 1-A: cj∈OjOj+1As shown in fig. 4:
① if
Figure BDA0001824744430000117
Then
Figure BDA0001824744430000118
Wherein
Figure BDA0001824744430000119
Is point AjX' coordinate value of，
Figure BDA00018247444300001110
Is point BjX' coordinate value of (a);
② if
Figure BDA00018247444300001111
Then
Figure BDA00018247444300001112
Wherein
Figure BDA00018247444300001113
Is point Fj,1The x' coordinate value of (a) is,
Figure BDA00018247444300001114
is point Fj,2X' coordinate value of (a); at point BjAs a circle center, LjMaking a circle with a radius, the intersection point of which with the arc is point Fj,1(ii) a At point AjAs a circle center, LjMaking a circle with a radius, the intersection point of which with the arc is point Fj,2；
③ if
Figure BDA00018247444300001115
Then
Figure BDA00018247444300001116
Case 1-B:
Figure BDA00018247444300001127
as shown in fig. 5:
① if
Figure BDA00018247444300001117
Then
Figure BDA00018247444300001118
② if
Figure BDA00018247444300001119
Then
Figure BDA00018247444300001120
Wherein, point Gj,1Is ray BjOjThe point of intersection with the incoming arc,
Figure BDA00018247444300001121
is point Hj,1The x' coordinate value of (a) is,
Figure BDA00018247444300001122
is point Hj,2X' coordinate value of (a); at point OjAs a circle center, Lj-RjMaking a circle with a radius, the intersection point of the circle and the arc is a point Hj,1(distance point A)jNearer) and point Hj,2(distance point A)jFarther);
③ if
Figure BDA00018247444300001123
Then
Figure BDA00018247444300001124
④ if
Figure BDA00018247444300001125
Then
Figure BDA00018247444300001126
Case 2: arc entry
Figure BDA0001824744430000121
Is minor arc and discharge arc
Figure BDA0001824744430000122
For the major arc, as shown in fig. 6:
① if
Figure BDA0001824744430000123
Then
Figure BDA0001824744430000124
② if
Figure BDA0001824744430000125
Then
Figure BDA0001824744430000126
③ if Lj>2RjThen, then
Figure BDA0001824744430000127
Case 3: arc entry
Figure BDA0001824744430000128
Is a major arc and a minor arc
Figure BDA0001824744430000129
Minor arc, as shown in fig. 7:
① if
Figure BDA00018247444300001210
Then omega1＝[-Rj+1,Rj+1]；
② if
Figure BDA00018247444300001211
Then
Figure BDA00018247444300001212
③ if
Figure BDA00018247444300001213
Then
Figure BDA00018247444300001214
Wherein
Figure BDA00018247444300001215
Is point Jj,2The x' coordinate value of (a) is,
Figure BDA00018247444300001216
is point Jj,3X' seat ofMarking a value; at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is a point Jj,1(distance point A)jNearer) and point Jj,2(distance point A)jFarther); at point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is a point Jj,3(distance point A)jNearer) and point Jj,4(distance point A)jFarther);
④ if Lj>2Rj+1Then, then
Figure BDA00018247444300001217
S302, according to the following conditions, calculating an x' coordinate set omega of a point on an arc, wherein the point meets the condition that the longest distance from the boundary of a handover area is not less than a navigation handover constraint threshold value2：
Case 1: discharge arc
Figure BDA00018247444300001218
And arc
Figure BDA00018247444300001219
Are minor arcs:
case 1-A: dj∈OjOj+1As shown in fig. 8:
① if
Figure BDA00018247444300001220
Then
Figure BDA00018247444300001221
② if
Figure BDA00018247444300001222
Then
Figure BDA00018247444300001223
Wherein
Figure BDA00018247444300001224
Is of point F'j,1The x' coordinate value of (a) is,
Figure BDA00018247444300001225
is of point F'j，2X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point F'j,1(ii) a At point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point F'j，2；
③ if
Figure BDA00018247444300001226
Then
Figure BDA00018247444300001227
Case 1-B:
Figure BDA00018247444300001329
as shown in fig. 9:
① if
Figure BDA0001824744430000131
Then
Figure BDA0001824744430000132
② if
Figure BDA0001824744430000133
Then
Figure BDA0001824744430000134
Wherein, point G'j,1Is ray BjOj+1The point of intersection with the outgoing arc,
Figure BDA0001824744430000135
is H'j,1The x' coordinate value of (a) is,
Figure BDA0001824744430000136
is H'j,2X' coordinate value of (a); at point Oj+1As a circle center, Lj-Rj+1Is a circle with a radius, and the intersection point of the circle and the arc is a point H'j,1(distance point A)jNearer) and point H'j,2(distance point A)jFarther);
③ if
Figure BDA0001824744430000137
Then
Figure BDA0001824744430000138
④ if
Figure BDA0001824744430000139
Then
Case 2: discharge arc
Figure BDA00018247444300001311
Is minor arc, entry arc
Figure BDA00018247444300001312
For the best fox, as shown in fig. 10:
① if
Figure BDA00018247444300001313
Then omega2＝[-Rj+1,Rj+1]；
② if
Figure BDA00018247444300001314
Then
Figure BDA00018247444300001315
③ if Lj>2Rj+1Then, then
Figure BDA00018247444300001316
Case 3: discharge arc
Figure BDA00018247444300001317
Is a major arc and a minor arc
Figure BDA00018247444300001318
For an inferior fox, as shown in fig. 11:
① if
Figure BDA00018247444300001319
Then omega2＝[-Rj,Rj]；
② if
Figure BDA00018247444300001320
Then
Figure BDA00018247444300001321
③ if
Figure BDA00018247444300001322
Then
Figure BDA00018247444300001323
Wherein
Figure BDA00018247444300001324
Is Point J'j,2The x' coordinate value of (a) is,
Figure BDA00018247444300001325
is Point J'j,3X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point J'j,1(distance point A)jNearer) and point J'j,2(distance point A)jFarther); at point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point J'j,3(distance point A)jNearer) and point J'j,4(distance point A)jFarther);
④ if Lj>2RjThen, then
Figure BDA00018247444300001326
S303, calculating omega1∪Ω2Is that is
Figure BDA00018247444300001327
And
Figure BDA00018247444300001328
the compressed value range of (a); and 4, planning a path based on the compressed area coding path planning space, and optimizing the position of the middle waypoint.
And 4, planning a path based on the compressed area coding path space obtained in the step 3, and optimizing the position of the middle waypoint.
The following describes a method for compressing a region coding path planning space of a moving body under multi-station relay navigation with reference to an embodiment. The following describes a method for compressing a region coding path planning space of a moving body under multi-station relay navigation with reference to an embodiment. As shown in fig. 12, the starting position of the moving body is (-0.5,0.6), the ending position is (6, -0.5), the moving body provides navigation information by six navigation station relays to reach the ending, and the positions of the navigation stations are, in order of navigation sequence: (0,0), (1.5,0.5), (2, -0.5), (3.6, -0.2), (4.5, -0.5) and (5.2,0), the radii of the effective ranges are 1, 1.1, 1.3, 1.1, 0.9 and 1.3, respectively, and the navigation handover constraint threshold is L ═ 1.3,1.9,1.3,1.2,1.5, in units.
The region-coding-based path can be represented as:
p＝[W1,W2,W3,W4,W5,W6,W7,W8,W9,W10]
＝[x'W1,y'W1,x'W2,y'W2,x'W3,y'W3,x'W4,y'W4,x'W5,y'W5,
x'W6,y'W6,x'W7,y'W7,x'W8,y'W8,x'W9,y'W9,x'W10,y'W10]
the value range before compression and the value range after compression of the waypoint x' coordinate are as follows:
Figure BDA0001824744430000141
in the experiment, a Differential Evolution (DE) algorithm is used as an optimization algorithm, the total length of a minimized path is used as a target function, navigation handover constraint is required to be met, and the position of a middle waypoint is optimized. DE-R denotes a path planning algorithm based on differential evolution and regional coding, and DE-R-K denotes a path planning algorithm based on differential evolution, regional coding and spatial compression. Firstly, setting the algorithm termination condition of DE-R and DE-R-K as the running time reaching 60 seconds to make them fully evolved, and regarding the smaller value of the objective function values of the optimum solution found by DE-R and DE-R-K as the objective function value f of the optimum solution*The value of the objective function is defined to be less than or equal to 1.05 × f*The solution of (2) is a better solution. Then, setting the algorithm termination conditions of DE-R and DE-R-K to find a better solution or the running time reaches 60 seconds, repeating the running for 30 times, and counting the probability of successfully finding the better solution and the average time of successfully finding the better solution of the two algorithms.
The experimental results are as follows: in 30 repeated experiments, the probability of successfully finding the better solution by DE-R is 50%, the average time of successfully finding the better solution is 48.1356 seconds, the probability of successfully finding the better solution by DE-R is 100%, and the average time of successfully finding the better solution is 28.2493 seconds. Obviously, DE-R-K is superior to DE-R, and the regional coding path planning space compression method of the moving body under multi-station relay navigation greatly compresses the value range of the road point abscissa, reduces the path planning space, and enables the optimization algorithm to find a better solution more quickly.
The embodiments disclosed above are implemented on the premise of the technical solution of the present invention, and detailed embodiments and specific operation procedures are given, but the scope of the present invention is not limited to the embodiments. From the above description, it should be understood that many modifications and substitutions may be made in the present invention, and all such modifications, equivalents, improvements and the like that are made on the basis of the technical solutions of the present invention are intended to be included in the scope of the present invention.

Claims (1)

1. A moving body path planning method under multi-station relay navigation based on space compression is characterized by comprising the following steps:
step 1, inputting a starting point position, an end point position, a navigation handover constraint threshold value, positions of a plurality of navigation stations and effective acting radiuses of a moving body; the effective range of the navigation station is represented by a circular area; defining the navigation handover constraint threshold as: in order to ensure the navigation handover success, the minimum path length of the moving body in the handover area is determined; the handover area is an overlapping area of effective action ranges of two navigation stations;
one path is formed by sequentially connecting waypoints comprising a starting point, a plurality of intermediate waypoints and a terminal point, and the waypoints are connected by adopting straight line segments; defining an intermediate waypoint comprising a starting junction and an ending junction of all the junction areas; the starting intersection point represents the position where the next navigation station starts to provide navigation information for the moving body, the ending intersection point represents the position where the previous navigation station stops providing navigation information for the moving body, and the navigation information of the moving body is provided by the two navigation stations together between the starting intersection point and the ending intersection point and the transfer of the navigation right of the moving body is completed; one path is jointly represented by the positions of all intermediate waypoints;
step 2, coding the intermediate waypoints by adopting a regional coding mode, wherein the starting intersection point and the ending intersection point are positioned at any positions in the intersection region;
defining two end points of an arc entering into the handover area, which are also two end points of an arc exiting out of the handover area, and the two end points are two top points of the handover area; establishing a local rectangular coordinate system by taking the middle point of a connecting line of two vertexes of the handover area as an origin, wherein the positive direction of the Y ' axis is the direction in which the position of the previous navigation station corresponding to the handover area points to the position of the next navigation station, and the positive direction of the X ' axis points to the right side from the left side of the Y ' axis; the positions of the start and end junctions are uniquely represented by two-dimensional coordinates (x ', y') in the local rectangular coordinate system;
respectively determining the value ranges of two coordinates of the starting junction and the ending junction:
wherein, the value range of the x' coordinate is as follows: under the local rectangular coordinate, if the arc entering and the arc exiting of the junction areaAre minor arcs, and the value range of the x' coordinate is
Figure FDA0002635064400000011
Wherein A and B are two vertices of the handover region; if one of the arc-in and arc-out is not inferior, the value range of the x' coordinate is [ -min (R)1,R2),min(R1,R2)](ii) a Wherein R is1And R2Effective acting radii of a navigation station and a next navigation station in a handover area are respectively;
the value range of the y' coordinate is as follows: taking projection points of the starting intersection point and the ending intersection point on an X ' axis as a vertical foot as auxiliary lines, intersecting two points with a boundary arc of an intersection area, wherein coordinate values of the two points on a Y ' axis are the maximum value and the minimum value of Y ' coordinates of the starting intersection point and the ending intersection point;
step 3, compressing the value ranges of the x' coordinates of the starting junction and the ending junction according to the geometric relation between the navigation cross-connection constraint threshold and the position and effective acting radius of the navigation station, and directly eliminating partial infeasible solutions violating the navigation cross-connection constraint;
step 4, based on the compressed area coding path space obtained in the step 3, path planning is carried out, and the position of the middle waypoint is optimized;
in step 3, the method for compressing the value ranges of the x' coordinates of the starting junction and the ending junction comprises the following steps:
s300, setting the positions of any two adjacent navigation stations as OjAnd Oj+1Radius is R respectivelyjAnd Rj+1Cross over to point AjAnd point BjPoint CjIs the mid-point of the arc, point DjIs the arc-out midpoint;
s301, calculating an x' coordinate set of points on an input arc, wherein the points meet the condition that the longest distance to the boundary of a handover area is not less than a navigation handover constraint threshold value:
case 1: the arc inlet and the arc outlet are minor arcs:
case 1-A: the mid point of the incoming arc is on the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint thresholdSatisfy the requirement of
Figure FDA0002635064400000021
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000022
Wherein
Figure FDA0002635064400000023
Is point AjThe x' coordinate value of (a) is,
Figure FDA0002635064400000024
is point BjX' coordinate value of (a);
② if the navigation handover constraint threshold is met
Figure FDA0002635064400000025
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000026
Wherein
Figure FDA0002635064400000027
Is point Fj,1The x' coordinate value of (a) is,
Figure FDA0002635064400000028
is point Fj,2X' coordinate value of (a); at point BjAs a circle center, LjMaking a circle with a radius, the intersection point of which with the arc is point Fj,1(ii) a At point AjAs a circle center, LjMaking a circle with a radius, the intersection point of which with the arc is point Fj,2；
③ if the navigation handover constraint threshold is met
Figure FDA0002635064400000029
Then the x' coordinate set of the point on the arc meeting the requirement that the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
case 1-B: the midpoint of the arc is not in the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint threshold is met
Figure FDA0002635064400000031
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000032
② if the navigation handover constraint threshold is met
Figure FDA0002635064400000033
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000034
Wherein, point Gj,1Is ray BjOjThe point of intersection with the incoming arc,
Figure FDA0002635064400000035
is point Hj,1The x' coordinate value of (a) is,
Figure FDA0002635064400000036
is point Hj,2X' coordinate value of (a); at point OjAs a circle center, Lj-RjMaking a circle with a radius, the intersection point of the circle and the arc is a point Hj,1And point Hj,2；
③ if the navigation handover constraint threshold is met
Figure FDA0002635064400000037
Then the longest distance to the boundary of the handover area on the incoming arc is satisfiedSet of x' coordinates of points at a distance not less than the navigation handover constraint threshold ″
Figure FDA0002635064400000038
④ if the navigation handover constraint threshold is met
Figure FDA0002635064400000039
Then the x' coordinate set of the point on the arc meeting the requirement that the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
case 2: the arc is inferior arc, and the arc is superior arc:
① if the navigation handover constraint threshold is met
Figure FDA00026350644000000310
The x' coordinate set of points on the arc that satisfy the "longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is [ -R [)j,Rj]；
② if the navigation handover constraint threshold is met
Figure FDA00026350644000000311
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA00026350644000000312
③ if the navigation handover constraint threshold satisfies Lj>2RjIf the distance to the boundary of the handover area is not less than the navigation handover constraint threshold, the x' coordinate set of the point on the arc is an empty set;
case 3: the arc is a major arc, and the arc is a minor arc:
① if the navigation handover constraint threshold is met
Figure FDA00026350644000000313
Then the arc is entered to satisfy the' edge to the handover areaThe set of x' coordinates of points whose longest distance of the boundary is not less than the navigation handover constraint threshold is [ -R [)j+1,Rj+1]；
② if the navigation handover constraint threshold is met
Figure FDA0002635064400000041
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000042
③ if the navigation handover constraint threshold is met
Figure FDA0002635064400000043
The x' coordinate set of the point on the arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000044
Wherein
Figure FDA0002635064400000045
Is point Jj,2The x' coordinate value of (a) is,
Figure FDA0002635064400000046
is point Jj,3X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is a point Jj,1And point Jj,2(ii) a At point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is a point Jj,3And point Jj,4；
④ if the navigation handover constraint threshold satisfies Lj>2Rj+1If the distance to the boundary of the handover area is not less than the navigation handover constraint threshold, the x' coordinate set of the point on the arc is an empty set;
s302, calculating an x' coordinate set of points on the arc, wherein the points meet the condition that the longest distance from the boundary of the handover area is not less than a navigation handover constraint threshold value:
case 1: the outgoing arc and the incoming arc are both minor arcs:
case 1-A: the midpoint of the arc is on the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint threshold is met
Figure FDA0002635064400000047
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000048
② if the navigation handover constraint threshold is met
Figure FDA0002635064400000049
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA00026350644000000410
Wherein
Figure FDA00026350644000000411
Is of point F'j,1The x' coordinate value of (a) is,
Figure FDA00026350644000000412
is of point F'j，2X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point F'j,1(ii) a At point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point F'j，2；
③ if the navigation handover constraint threshold is met
Figure FDA00026350644000000413
Then "to the boundary of the handover area" is satisfied on the outgoing arcThe x' coordinate set of the point of which the longest distance is not less than the navigation handover constraint threshold is an empty set;
case 1-B: the midpoint of the arc is not in the line segment OjOj+1The method comprises the following steps:
① if the navigation handover constraint threshold is met
Figure FDA0002635064400000051
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000052
② if the navigation handover constraint threshold is met
Figure FDA0002635064400000053
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000054
Wherein, point G'j,1Is ray BjOj+1The point of intersection with the outgoing arc,
Figure FDA0002635064400000055
is H'j,1The x' coordinate value of (a) is,
Figure FDA0002635064400000056
is H'j,2X' coordinate value of (a); at point Oj+1As a circle center, Lj-Rj+1Is a circle with a radius, and the intersection point of the circle and the arc is a point H'j,1And point H'j,2；
③ if the navigation handover constraint threshold is met
Figure FDA0002635064400000057
Then the longest distance to the boundary of the handover area on the outgoing arc satisfies "is not less than the navigation handover constraint threshold"is a set of x' coordinates of points
Figure FDA0002635064400000058
④ if the navigation handover constraint threshold is met
Figure FDA0002635064400000059
Then the x' coordinate set of the point on the outgoing arc which meets the condition that the longest distance from the boundary of the handover area is not less than the navigation handover constraint threshold value is an empty set;
case 2: the arc outlet is a minor arc, and the arc inlet is a major arc:
① if the navigation handover constraint threshold is met
Figure FDA00026350644000000510
The x' coordinate set of points on the outgoing arc that satisfy "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is [ -Rj+1,Rj+1]；
② if the navigation handover constraint threshold is met
Figure FDA00026350644000000511
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA00026350644000000512
③ if the navigation handover constraint threshold satisfies Lj>2Rj+1If so, the x' coordinate set of the point on the outgoing arc meeting the condition that the longest distance from the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
case 3: the outgoing arc is a major arc, and the incoming arc is a minor arc:
① if the navigation handover constraint threshold is met
Figure FDA0002635064400000061
The longest distance to the boundary of the handover area on the outgoing arc that satisfies "is not less than the navigationThe x' coordinate set of points of the handover constraint threshold "is [ -R ]j,Rj]；
② if the navigation handover constraint threshold is met
Figure FDA0002635064400000062
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000063
③ if the navigation handover constraint threshold is met
Figure FDA0002635064400000064
The x' coordinate set of the point on the outgoing arc that satisfies "the longest distance to the boundary of the handover area is not less than the navigation handover constraint threshold" is
Figure FDA0002635064400000065
Wherein
Figure FDA0002635064400000066
Is Point J'j,2The x' coordinate value of (a) is,
Figure FDA0002635064400000067
is Point J'j,3X' coordinate value of (a); at point BjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point J'j,1And point J'j,2(ii) a At point AjAs a circle center, LjIs a circle with a radius, and the intersection point of the circle and the arc is point J'j,3And point J'j,4；
④ if the navigation handover constraint threshold satisfies Lj>2RjIf so, the x' coordinate set of the point on the outgoing arc meeting the condition that the longest distance from the boundary of the handover area is not less than the navigation handover constraint threshold is an empty set;
and S303, calculating a union of the two x 'coordinate sets obtained in the steps S301 and S302, namely a value range after compression of the x' coordinates of the starting junction and the ending junction.
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